Running OBD 1 or 2 engines OBD 0?

Im looking to replace my LS with a newer LS and I was wondering if it's ok to run an obd I or obd II LS engine as an OBD 0 engine or should I convert to a later OBD?

The giant Swap info thread says you can run them OBD 0 by using an OBD 0 ECU and dizzy (wich I already have running my current LS engine. Is this really an optimal way to run the engine or would I have to have my ECU remapped.

I ask because it seems really easy to find OBD II LS engines as opposed to older OBD 0 engines. Plus a newer engine is more likely to have less miles on it.

But it wont necessarily hurt the motor to run it with my OBD 0 equipment?

I'm just looking to get something and rebuild it to stock specs and make a nice reliable (but still fun) daily for myself with some weekend autox possibly in the summer (non-competitively, I just want to do it for fun). Plus I want the learning experience of rebuilding a motor.

I have looked in to the OBD I conversion and it doesn't look terribly difficult. I would just have to convert the plugs for an OBD 1 dizzy, get a jumper harness for the OBD I ecu and wire for a four wire O2 sensor?